A113065 - OEIS

A113065

a(n) = denominator of r(n), where r(n) = the continued fraction of rational terms [1,3/2,11/6,...,H(n)], where H(n) = sum{j=1..n} 1/j, the n-th harmonic number.

%I #9 Apr 09 2014 10:16:31

%S 1,3,45,1341,216117,12198933,5033340279,4308570125919,

%T 34267321328538951,280288242453582014931,25856932235044095350623341,

%U 2439612204830872620697726926561,3054068039108858195570513558702127273

%N a(n) = denominator of r(n), where r(n) = the continued fraction of rational terms [1,3/2,11/6,...,H(n)], where H(n) = sum{j=1..n} 1/j, the n-th harmonic number.

%e For n = 3 we have 1 + 1/(3/2 + 6/11) = 67/45, the denominator of which is 45.

%o ;;PLT DrScheme (Joshua Zucker)

%o ;;(harmonic n) gives the n-th partial sum of the harmonic series.

%o ;;cf->frac is a utility that converts a continued fraction to a fraction.

%o (define (A113065 n)

%o (denominator (cf->frac (build-list n (lambda (k) (harmonic (add1 k)))))))

%Y Cf. A113064, A001008, A002805.

%K frac,nonn

%O 1,2

%A _Leroy Quet_, Oct 13 2005

%E More terms from _Joshua Zucker_, May 08 2006